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Chemical Kinetics

1. Rate Laws and Order

Kinetics describes how fast a reaction occurs. The rate law is determined experimentally: $Rate = k[A]^x[B]^y$.

  • Order: The sum $x+y$. It can be fractional or zero.
  • Molecularity: The number of reacting species in an elementary step. It is always a whole number (1, 2, or 3).

2. Integrated Rate Equations

First Order Reactions: Most common in exams. $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$. The half-life $t_{1/2} = \frac{0.693}{k}$ is independent of initial concentration.

Interactive diagram: open this page in a browser to use it.

3. Temperature Dependence

The Arrhenius Equation: $k = A e^{-E_a/RT}$. As temperature increases, the fraction of molecules with energy $\ge E_a$ increases exponentially, leading to a much faster rate.

⚡ Quick Hack

For every $10^\circ C$ rise in temperature, the rate constant approximately doubles. This is known as the Temperature Coefficient (typically 2 to 3).

4. Zero-Order Reactions

Rate is independent of concentration: $[A]_t = [A]_0 - kt$. The half-life $t_{1/2} = \frac{[A]_0}{2k}$ is proportional to the initial concentration. Examples: decomposition of $NH_3$ on a hot platinum surface, and $HI$ on gold, at high pressure.

5. Units of $k$ and Half-lives

  • Zero order: $mol\,L^{-1}s^{-1}$; $t_{1/2} \propto [A]_0$.
  • First order: $s^{-1}$; $t_{1/2}$ is independent of $[A]_0$.
  • Second order: $L\,mol^{-1}s^{-1}$; $t_{1/2} \propto 1/[A]_0$.
  • General: units of $k$ are $(mol\,L^{-1})^{1-n}s^{-1}$ for order $n$.

For a first-order reaction, the time for 99.9% completion is about 10 half-lives, and the time for 99% completion is twice the time for 90% completion.

6. Pseudo-First-Order Reactions

When one reactant is in large excess, its concentration barely changes and the reaction behaves as first order. Acid hydrolysis of ethyl acetate and the inversion of cane sugar are classic examples.

7. Arrhenius Equation in Two-Temperature Form

$$\log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\left(\frac{T_2 - T_1}{T_1 T_2}\right)$$

A plot of $\ln k$ against $1/T$ is a straight line of slope $-E_a/R$. A catalyst lowers $E_a$ for both the forward and the reverse reaction; it does not change $\Delta H$ or the equilibrium constant.

8. Collision Theory

Only collisions with energy at least $E_a$ and the right orientation lead to products. Rate $= P Z_{AB} e^{-E_a/RT}$, where $P$ is the steric (probability) factor.

Practice questions

  1. The half-life of a first-order reaction is 10 min. The time taken for 75% completion is:

    1. 10 min
    2. 15 min
    3. 20 min
    4. 30 min
    Answer

    C. 75% completion = two half-lives = 20 min.

  2. The unit of the rate constant for a zero-order reaction is:

    1. s⁻¹
    2. mol L⁻¹s⁻¹
    3. L mol⁻¹s⁻¹
    4. L²mol⁻²s⁻¹
    Answer

    B. For order n, units are (mol L⁻¹)¹⁻ⁿs⁻¹; with n = 0, mol L⁻¹s⁻¹.

  3. For a first-order reaction, k = 0.693 × 10⁻²\ min⁻¹. Its half-life is:

    1. 1 min
    2. 10 min
    3. 100 min
    4. 69.3 min
    Answer

    C. t₁/₂ = 0.693/k = 0.693/(0.693 × 10⁻²) = 100 min.

  4. A catalyst increases the rate of a reaction by:

    1. Increasing Δ H
    2. Lowering the activation energy
    3. Increasing the equilibrium constant
    4. Increasing the temperature
    Answer

    B. A catalyst provides an alternative pathway with lower Eₐ; Δ H and K are unchanged.

  5. The acid hydrolysis of ethyl acetate in excess water is:

    1. Zero order
    2. Pseudo first order
    3. Second order in water
    4. Third order
    Answer

    B. Water is in large excess, so its concentration is effectively constant and the rate depends only on the ester.

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